HOL4 vs Rocq

HOL4 is a free, interactive proof assistant for higher-order logic, with a programming environment for proving theorems and building proof tools. It supports work that combines deduction, execution, and property checking. Built-in decision procedures and theorem provers can establish many simple theorems, and an oracle mechanism can connect to external programs such as SMT and BDD engines. HOL4 supports higher-order logic and Standard ML, and can produce proof artifacts and counterexamples. It is self-hosted and listed for Linux, macOS, and Windows. A Standard ML compiler is required, with Poly/ML recommended; Moscow ML and MLTon are also supported for building tool executables. Windows installation can use Cygwin or the Windows Linux subsystem with Poly/ML. Moscow ML is another option, but the Windows guide notes that it is slower, lacks some Poly/ML libraries, and cannot run concurrent Holmake builds. HOL includes Emacs modes for syntax display and session interaction, and the installation guide links to Vim plugin documentation. Online materials include a tutorial, quick reference, FAQ, manuals, and generated indexes.

Rocq is a free interactive theorem prover and proof assistant for building mathematical proofs, formal specifications and programs, including proofs that programs meet specifications. Its Gallina language supports specification and mathematical work and is based on the Polymorphic, Cumulative Calculus of Inductive Constructions. A relatively small certification kernel machine-checks proofs. Rocq also offers interactive proof methods, decision and semi-decision algorithms, and a tactic language for defining methods. Certified programs can be extracted to OCaml, Haskell or Scheme, and the system can connect with external computer algebra systems or theorem provers. The Rocq Platform bundles the core prover with libraries and plugins for development and teaching. Its scripts install Rocq and packages on macOS, Windows and many Linux distributions; precompiled installers are available for macOS and Windows, but not Linux. Editor options include the VsRocq Visual Studio Code extension, RocqIDE, Proof General and Coqtail. Rocq is written in OCaml and distributed under the GNU Lesser General Public Licence Version 2.1.